Flask+React系统中注册新用户后无法立即创建会话，需重新登录才生效的问题求助

我现在用React做前端，Flask+SQL做后端实现了登录/注册表单，目前登录、登出功能都正常，会话也能正常创建。但遇到一个头疼的问题：新用户注册的时候，所有流程都走得很顺畅——能创建新用户名、密码这些，也能直接访问需要权限的路由，但注册完成后并没有立即创建会话，必须先登出再重新登录，会话和Cookie才会正常生成。

下面是我的相关代码：

Flask后端注册路由 #

class Signup(Resource):
    def post(self):
        form_json = request.get_json()
        username = form_json.get("username")
        email = form_json.get("email")
        password = form_json.get("password")

        # Check if all required fields are provided
        if not username or not email or not password:
            return make_response({"error": "All fields are required: username, email, password"}, 400)

        # Check if the username or email already exists
        if User.query.filter_by(username=username).first():
            return make_response({"error": "Username already taken"}, 400)
        if User.query.filter_by(email=email).first():
            return make_response({"error": "Email already registered"}, 400)

        try:
            new_user = User(username=username, email=email)
            new_user.password = password  # Use password setter for hashing
            db.session.add(new_user)
            db.session.commit()

            # Automatically sign in the new user
            session["user_id"] = new_user.id
            return make_response(new_user.to_dict(), 201)
        except Exception as e:
            return make_response({"error": str(e)}, 500)
        
api.add_resource(Signup, '/signup')

React前端用户上下文（包裹整个应用） #

import { createContext, useEffect, useState } from "react";

export const UserContext = createContext();

export const UserProvider = ({ children }) => {
  const [user, setUser] = useState(null);

  useEffect(() => {
    fetch("/check_session").then((response) => {
      if (response.ok) {
        response.json().then((user) => setUser(user));
      } else {
        setUser(null);
      }
    });
  }, []);

  const checkSession = () => {
    return fetch("/check_session", { credentials: "include" }).then(
      (response) => {
        if (response.ok) {
          return response.json().then((user) => {
            setUser(user);
            return user;
          });
        } else {
          setUser(null);
          throw new Error("No active session");
        }
      }
    );
  };

  useEffect(() => {
    checkSession().catch((error) =>
      console.log("No active session on load:", error)
    );
  }, []);

  const logInUser = (loginData) => {
    return fetch("/login", {
      method: "POST",
      headers: {
        "Content-Type": "application/json",
      },
      body: JSON.stringify(loginData),
      credentials: "include",
    }).then((response) => {
      if (response.ok) {
        return response.json();
      } else {
        throw new Error("Login failed");
      }
    });
  };

  const logOutUser = () => {
    return fetch("/logout", { method: "DELETE", credentials: "include" }).then(
      (response) => {
        if (response.ok) {
          setUser(null);
        } else {
          throw new Error("Logout failed");
        }
      }
    );
  };

  return (
    <UserContext.Provider
      value={{ user, setUser, logInUser, logOutUser, checkSession }}
    >
      {children}
    </UserContext.Provider>
  );
};

我想要的效果是：用户注册完成后，自动登录的同时就能创建好会话，不用再手动登出登录一次。有没有大佬能帮忙看看问题出在哪？

备注：内容来源于stack exchange，提问作者Big McLargehuge